"Bake" all Particle systems into their object
You can turn particles into real objects with the convert button in the particles modifier panel.

In this case I think what you may be looking for is BVH caching. Under Render Properties there is a Performance panel. There you will find an option to cache BVH. Blender internal has some different options.

From the 2.62 Release notes -


  For renders where only the camera or materials are changing, while meshes stay fixed, it is now possible to skip the sometimes slow BVH step, by enabling BVH Cache in the Performance panel. This will store the BVH on disk for subsequent (animation) renders of the same scene. Note that if the scene does change in the animation, enabling this option will make rendering somewhat slower.


From your sample animation this may not help as the mesh objects in the scene appears to be changing, unless you are making the materials transparent. If you do have this enabled then maybe disabling it will help.

One possibility may be to render the background animation and then composite the shed animation onto it. Another is to animate material transparency instead of object visibility.